RE: Quantum Rebel

From: Fred Chen <>
Date: Sat, 14 Aug 2004 16:56:12 -0700

Russell, I agree with what you state below. But consider the following

Instead of two beams of equal intensity interfering, as in classical
inteferometry, one has unequal amplitude beams. Specifically,

Beam A: 0.9*exp(iax+ibz-iwt)
Beam B: 0.1*exp(-iax+ibz-iwt)

The interference pattern is of the form:

Interference field = [cos(ax)+i*0.8sin(ax)]exp(ibx-iwt)

So the resulting photon distribution follows the intensity, or the field
amplitude squared:

Interference intensity = 0.64+ 0.36*cos^2(ax)

This wave pattern will begin to appear after sufficient number of
photons, but each photon is always ~99% (81/82) likely to have
originated from Beam A, based on conservation.

If Beam A and Beam B had different amplitudes, you would maximize the
uncertainty of the photon origin since you have to say 50/50 likelihood
for a photon coming from either A or B.

The complementarity principle's strongest statement is 100% certainty,
and that cannot be attained. But we can still get an idea of the wave
interference pattern and 'which way' information with high (but not
100%) certainty in gray-transition cases such as above.


-----Original Message-----
From: Russell Standish []
Sent: Saturday, August 14, 2004 2:51 AM
To: Fred Chen
Cc: 'Everything List'
Subject: Re: Quantum Rebel

On Fri, Aug 13, 2004 at 11:43:10PM -0700, Fred Chen wrote:

> A better (and far simpler) way to challenge complementarity would be
> to use a low-intensity interferogram in a photographic film or CCD. At

> first the photons being detected are few so the shot (particle-like)
> aspect is more obvious. As more photons are integrated, the classical
> interference pattern is observed. Can there be a transition region
> where both aspects are observable?

This does not challenge complementarity. Consider a double slit
apparatus with the photon source's intensity down so low that each
individual photon can be observed hitting the screen one at a time. But
when one plots the distribution of positions where the photons strike
the screen after observing many of them, the interference pattern
results. This is simple and uncomplicated, but is not what the
complementarity principle is about.

Now consider that you have information about which slit the photon
passed through before hitting the screen - ie each photon is labelled 1,
2, 1, 1, etc, according to whuch slit it passed through. Therefore, you
can separate the observed photons into two sets, according to which slit
the phtons passed through. The distribution of each subset corresponds
to a single slit experiment, and the final distribution must be the sum
of the two single slit experiements. But single slit experiments do not
have interference patterns - hence the sum cannot have an interference
pattern either.

Consequently, if you have any way of knowing which slit the photon went
through (the "which way" information), then you cannot have an
interference pattern. This is what the complementarity principle means.

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Received on Sat Aug 14 2004 - 19:59:57 PDT

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